Linear Algebra :¶
- It help us to understand the higher dimesional (4D,5D etc) space using mathematical tools we need .
- It generalized the 2D and 3D to higher dimenional
- Basic Concepts in Linear Algebra :
* Point or Vector
Distance of a point from origin :
Distance between two Points :
Some terminology : Row vectore, Column Vector, Matrix
Matrix Operation : Vector Addition ,Vector Multiplication (Dot product, Cross product)
- Cross product is not much more used in ML
Geomertical meaning of dot product :
Projection and Unit Vector :
Unit Vector : It is the vector in same direction having length is unity
Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane -- Lecture10.5 missed
Distance of a point from a PlaneHyperplane, Half-Spaces :
- distance of a point from a plane
- A line divides the 2-D space into two parts
- A plane divided the 3-D space into two parts
- A hyper-plance divides the 4-D or higher dimensional space into two parts , these two parts are called hyper-space
Equation of a circle(2D), Equation of Sphere(3D), Equation of Hypersphere(n-D):
Q .How to determine a point is inside circle/sphere/hypersphere or outside ?
Ans : Circle also divides the region into two space , We will determine using below conditions :-
Equation of a Ellipse(2D), Equation of Ellipsoid(3D), Equation of Hyper-Ellipsoid(n-D):
Ellipse are not much more used in ML , generally we used planes & circles.
Square & Rectangle :
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